Mott localization in the correlated superconductor Cs3C60 resulting from the molecular Jahn-Teller effect
Katalin Kamaras, Gyongyi Klupp, Peter Matus, Alexey Y. Ganin, Alec McLennan, Matthew J. Rosseinsky, Yasuhiro Takabayashi, Martin T. McDonald, Kosmas Prassides
aa r X i v : . [ c ond - m a t . s t r- e l ] M a r Mott localization in the correlated superconductorCs C resulting from the molecular Jahn-Teller effect Katalin Kamar´as , Gy¨ongyi Klupp , P´eter Matus , Alexey Y.Ganin , Alec McLennan , Matthew J. Rosseinsky , YasuhiroTakabayashi , Martin T. McDonald , Kosmas Prassides Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, HungarianAcademy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary Department of Chemistry, University of Liverpool, Liverpool L69 7ZD, UK Department of Chemistry, Durham University, Durham DH1 3LE, UKE-mail: [email protected]
Abstract. Cs C is a correlated superconductor under pressure, but an insulator under ambientconditions. The mechanism causing this insulating behavior is the combination of Mottlocalization and the dynamic Jahn-Teller effect. We show evidence from infrared spectroscopyfor the dynamic Jahn-Teller distortion. The continuous change with temperature of the splittingof infrared lines is typical Jahn-Teller behavior, reflecting the change in population of solid-stateconformers. We conclude that the electronic and magnetic solid-state properties of the insulatingstate are controlled by molecular phenomena. We estimate the time scale of the dynamic Jahn-Teller effect to be above 10 − s and the energy difference between the conformers less than 20cm − .
1. Introduction
Trivalent fulleride salts belong to the family of correlated superconductors, similar tohigh temperature superconducting cuprates [1, 2]. They show a dome-shaped T c (superconducting transition temperature) versus lattice constant phase diagram [3] with anantiferromagnetic insulating state above a critical lattice constant [1]. The transition frommetallic/superconducting to insulating behavior is generally attributed to Mott localization.Fullerides showing similar behavior have been known for a long time. Metallic fcc (face centeredcubic) mixed alkali Cs x A (3 − x ) C (A=K,Rb) phases have been prepared, which were in thelattice constant range where T c decreases upon expansion [4]. Guest molecules, like cubane [5] orammonia [6] were also used to expand the lattice. This approach leads in most cases to a changein crystal structure, inducing a crystal field with lower symmetry which distorts the fulleridemolecular ions. Metal-insulator transitions in these compounds have been confirmed [7, 8],but since these occur in a low-symmetry crystal field, the external and internal contributionscould not be unambiguously distinguished. Cs C is in this respect a key compound. It is anexpanded structure, shows a metal-to-insulator transition upon application of pressure [3, 9] andretains its cubic structure in the whole pressure range.Cs C has two cubic polymorphs, an ordered A15 [3] and a merohedrally disordered fcc one[10]. At ambient pressure they are insulators and magnetic with S=1/2, but turn into metalspon application of pressure [11], exhibiting superconducting transition temperatures T c up to38 K [3]. The metal-insulator transition upon increasing distance between the fulleride ions andthe localized magnetic moments point to strong electron-electron correlation and consequently,Mott localization.The localization mechanism was suggested to involve a Jahn-Teller distortion [12], which isdifficult to prove experimentally. Atomic displacements in the distorted molecular ions havebeen estimated to fall in the range of 0.05 ˚angstroms, hard to detect even by sensitive neutronscattering experiments. However, since the distortion involves a symmetry change, vibrationalspectroscopy can be a sensitive indicator. The T u (4) infrared-active mode at 1429 cm − ismost widely used to detect both charge and symmetry changes in C [13]. From symmetryconsiderations for an I h point group object placed in a cubic environment, it follows that thismode will not show splitting caused by the environment. Therefore, all splittings found can bedirectly related to the symmetry reduction following from the molecular Jahn-Teller effect.
2. The Jahn–Teller effect in solid fullerides E po t Q(b) (c) E po t Q E po t Q E po t Q (f)(e)(d)(a) E po t Q E po t Q Figure 1.
Possible potential energy surfaces of the C − molecular ion in Cs C . (a) Thepossible D h distortions in all directions have the same energy. (b) No energy barrier betweendifferently directed distortions causes an average I h symmetry. (c, e, f) Two inequivalentdirections of differing energy separated by a small energy barrier. (c) Static distortion in oneof the directions. (d) Two inequivalent directions of similar energy separated by a large energybarrier. A small energy difference between the two wells is possible. Static distortion. (e)Dynamic distortion with two solid-state conformers with differing population. (f) Hinderedpseudorotation between differently directed distortions.According to theoretical calculations [14] the symmetry of the Jahn–Teller distortion of C − isD h . The potential energy surface of a single distortion is schematically illustrated in Fig. 1 (a).The possible combinations of fifteen equivalent twofold axes among the symmetry elements oficosahedral C define thirty equivalent distortions among which the molecule can move. Thecorresponding motion is called pseudorotation (see the movie in the Supplementary Information).The molecule performing pseudorotation is dynamically distorted. If there is no barrier betweenthe different D h distortions (free pseudorotation), the molecular symmetry will be restored toI h in time average [15] (see Fig. 1 (b)). Introducing a barrier between the D h distortions resultsin hindered pseudorotation [15] (see Fig. 1 (e) and (f)). If the time scale of a spectroscopiceasurement is shorter than that of pseudorotation, the D h distortion can be detected. Thetime scale of infrared excitations being of the order of 10 − s, spectra corresponding to distortedstates correspond to pseudorotations slower than this value. The last possibility is that with abarrier high enough to cause static distortion along one special axis [15] (see Fig. 1 (c) and (d)).In the solid one has to take into account the effect of the crystal field determined by thepotential created by the neighboring Cs + ions. The undistorted site symmetry is T h in thesecubic crystals, so the crystal field alone would not lower the symmetry of the fulleride ions belowthat point group.[16]. The number of twofold axes along which Jahn-Teller distortion can occuris reduced to three, and if one considers the C − ion in a T h point group there will be just twoinequivalent directions. This is why two kinds of distortions appear in Fig. 1 (c)-(f).Thermal expansion results in weaker crystal field acting towards equalizing the two kinds ofdistortions. In addition, at higher temperature the higher energy states become increasinglypopulated. Thus, for example, heating will lead from the state in Fig. 1 (c) to (e), and furtherto (f). Raising the temperature will also lower the barriers between potential energy wells (bestseen in Fig. 1 (d)) and they can be more easily overcome.
3. Experimental
The Cs C samples used in this study were prepared by solution chemistry routes as describedelsewhere [3, 10]. Sample composition and structure were determined by x-ray diffraction.Infrared measurements were done on both fcc-rich and A15-rich materials, in KBr pellets with0.25 cm − resolution [16].
4. Signatures of the Mott insulating state
600 800 1000 1200 14000.00.20.40.60.81.0 600 800 1000 1200 1400 0.00.20.40.60.81.0 fcc Cs C A15 Cs C Rb C C T r an s m i ss i on Wavenumber (cm -1 ) Figure 2.
Infrared spec-trum of A15 and fcc Cs C in the range of intramolecu-lar vibrations at room temper-ature. The room temperaturespectra of insulating C andmetallic Rb C are includedfor comparison. The metalliccharacter influences both thebackground and the lineshape.The measured infrared spectra of both polymorphs together with that of C and of metallicRb C are shown in Fig. 2. The spectrum of pure C consists of four lines, a consequence ofthe high symmetry of the fullerene ball [17]. In accordance with previous data [18], the highestfrequency mode softens due to the charge added on the fullerene, showing approximately thesame shift in Cs C and in Rb C . The lineshape of this mode, however, is different forRb C and for Cs C . Rb C has a Fano lineshape [19] as a consequence of coupling betweenvibrational states and the electronic continuum of the same energy. The non-Fano lineshape inboth polymorphs of Cs C signals the absence of metallic electrons, therefore these materialsare insulators, in agreement with previous measurements [1]. Metallic electrons also cause aontinuous background absorption, which is indeed present in Rb C , but not in either of thetwo Cs C polymorphs.Another signature of the insulating state is that it facilitates the appearance of the Jahn–Tellereffect: molecular ions can suffer a Jahn–Teller distortion only if their electrons are localized.The asymmetrically broadened lineshape in both Cs C compounds (Fig. 2) indicates splittingof the vibrational lines, a consequence of the symmetry reduction owing to the Jahn–Tellerdistortion [16]. To further study the temperature and the polymorph dependence of the splitting,temperature dependent measurement were performed on both Cs C polymorphs.
5. Jahn–Teller effect in Cs C
500 600 700 800 900 1000 1100 1200 1300 1400
A15 Cs C
28 K 54 K 81 K110 K140 K170 K200 K233 K264 K300 K345 K390 K T r an s m i ss i on ( a r b . u . ) Wavenumber (cm -1 )
28 K110 K 200 K300 K 390 K T r an s m i ss i on ( a r b . u . ) Wavenumber (cm -1 ) Figure 3.
Temperature-dependent IR spectra of A15Cs C (left: full spectrum,right: range of T u (4) andG u (6) modes). The splittingchanges gradually.Figures 3 and 4 illustrate the gradual changes in the splitting, characteristic of bothpolymorphs (although not exactly identical). Newly activated low intensity modes between 600-800 cm − can also be observed at low temperature. These changes indicate that the symmetrylowering is different in the two Cs C polymorphs. The weak new modes disappear at differingtemperatures underlining the smooth nature of the transition. As we will see, this is a sign oftemperature-dependent solid-state conformers, implying a dynamical Jahn–Teller effect [15].The low-temperature multiple peak structure and its dependence on crystal structure is aresult of the interplay between crystal field and Jahn–Teller distortion. The Cs + ions thatsurround the C − ion constitute a cubic environment and do not cause splitting in the T u modes. However, the energies of molecular distortions, that are equivalent in a free molecularion, can differ slightly in a crystal when pointed at different crystallographic directions. Theobservation of the signatures of the Jahn–Teller distortion in the vibrational spectra rules outthe case of Fig. 1 (b) (free pseudorotation). Statically ordered distortions in the lattice with thesame energy (Fig. 1 (a)) would lead to a temperature-independent spectrum consisting of one setof lines (maximum 3+4, for triply degenerate T u and quadruply degenerate G u , respectively)and is also contrary to observation. The number of possible allowed IR lines (in principle 1* or2*(3+4)) corresponds to the number of populated potential energy wells (1 in Fig. 1 (a-c) and2 in Fig. 1 (d-f)). According to the experiments, this number continously decreases on heating.This finding can be qualitatively explained by a model where the population of the wells changeswith temperature.
00 600 700 800 900 1000 1100 1200 1300 1400 fcc Cs C
27 K 41 K 56 K 81 K113 K144 K171 K200 K230 K260 K290 K320 K T r an s m i ss i on ( a r b . u . ) Wavenumber (cm -1 )
27 K 81 K 171 K260 K 320 K T r an s m i ss i on ( a r b . u . ) Wavenumber (cm -1 ) Figure 4.
Temperature de-pendent IR spectra of fccCs C . The splitting changesgradually.The simplest of these models is that of the static-to-dynamic transition (from Fig. 1 (d)to (f)) on heating. At low temperature the differently directed distortions would be frozen inwith static and disordered distortion. Thermal expansion lowers the barrier and the increasedthermal energy from pseudorotation helps to overcome it. In this case the transition would belocated in a considerably narrower temperature range, but we observe a continuous change overthe whole temperature range we measured. The model based on Fig. 1 (d), where the barrier istoo high for a transition even at high temperature, can also be rejected based on the measuredtemperature-dependent infrared data. A transition could also happen from the static distortionshown in Fig. 1 (c) to the dynamic ones Fig. 1 (e) and (f). The number of lines should firstincrease on heating, then start to decrease. As we cannot prove such a behaviour, this case canalso be ruled out.This leaves us with the dynamic distortions Fig. 1 (e) and (f), the latter developing from theformer on increasing temperature. This situation corresponds to different solid-state conformerswith different occupational probability [16]. On heating, both their energy difference and theirpopulational difference gradually disappears [15], as observed in the spectra. Fewer kinds ofdistortions mean fewer lines in the infrared spectra. The two equilibrium conformations with alow barrier (Fig. 1e) are connected by hindered pseudorotation [15]. The fact that we observethe distorted states puts the lower limit of the time scale of this pseudorotation to 10 − s, andthe lowest temperature being 28 K can be reconciled with an upper limit of 20 cm − for thebarrier between the two conformers.
6. Conclusions
We studied the temperature-dependent infrared spectra of both polymorphs of the correlatedsuperconductor Cs C in their normal state. The vibrational signatures reveal the insulatingstate of these materials, and establish the interplay of Mott localization and the Jahn-Tellereffect in forming this state. In addition, the crystal field influences the vibrational levels makingthe spectra temperature- and polymorph-dependent. The presence of temperature-dependentsolid-state conformers validates the proof of the dynamic Jahn–Teller effect. Acknowledgments
Funding for this research was provided by the Hungarian National Research Fund (OTKA)(Grant No. 75813), the Engineering and Physical Sciences Research Council(Grant No.P/G037132 and EP/G037949), and the EU-Japan project LEMSUPER (Grant No. NMP3-SL-2011-283214).
Supplementary Information accompanies this paper.
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